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On Topological Properties of Some Coverings. An Addendum to a Paper of Lanteri and Struppa

Published online by Cambridge University Press:  20 November 2018

Jarosław A. Wiśniewski
Jarosław A. Wiśniewski*
Affiliation:
Warsaw University, Institute of Mathematics, ul. Banacha 2, 00-913 Warszawa, Poland
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Abstract

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Let π: X′ → X be a finite surjective morphism of complex projective manifolds which can be factored by an embedding of X′ into the total space of an ample line bundle 𝓛 over X. A theorem of Lazarsfeld asserts that Betti numbers of X and X′ are equal except, possibly, the middle ones. In the present paper it is proved that the middle numbers are actually non-equal if either 𝓛 is spanned and deg π ≥ dim X, or if X is either a hyperquadric or a projective space and π is not a double cover of an odd-dimensional projective space by a hyperquadric.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 1 , 01 December 1991 , pp. 206 - 214
Copyright
Copyright © Canadian Mathematical Society 1989

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